The homology of ``\(k\)-equal'' manifolds and related partition lattices
This paper analyzes the topology of the spaces \(V(n,k)\) consisting of sets of points \((x_1,\dots, x_n)\) in \(\mathbb{R}^n\) (or \(\mathbb{C}^n\)) which satisfy \(x_{x_1} = x_{i_2} = \dots = x_{i_n}\) for some set of \(k\) indices, and \(M(n,k) = \mathbb{R}^n - V(n,k)\) (or \(\mathbb{C}^n - V(n,k)\)). The \(M(n,k)\) are the ``\(k\)-equal'' manifolds of the title. For \(k = 2\), these spaces have been much studied, so the emphasis is on larger \(k\) values. The results generally say that the cohomology is free abelian, and the ranks are determined.
scientific article; zbMATH DE number 745285